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In this paper we have studied the effect of external magnetic field in theco-existing phase of superconducting and anti-ferromagnetism of rare earthnickel borocarbides. The anti-ferromagnetism in these systems might haveoriginated due to both localized 'f' electrons as well as itinerant electronswhich are responsible for conduction. On the other hand, superconductivity isdue to spin density wave, arising out of Fermi surface instability. Theanti-ferromagnetism order is mostly influenced by hybridization of the 'f'electron with the conduction electron. Here we have obtained the dependence ofsuperconducting energy gap as well as staggered magnetic field on temperature Tand energy $\epsilon_k$ in a framework based on mean field Hamiltonian usingdouble time electron Green's function. We have shown in our calculation theeffect of external magnetic field on superconducting and anti-ferromagneticorder parameter for $YNi_2B_2C$ in the presence of hybridization. The ratio ofthe calculated effective gap and $T_C$ is close to BCS value which agrees quitewell with experimental results.

Effect of External Magnetic Field on the Co-existence of Superconductivity and Antiferromagnetism in rare Earth Nickle Borocarbides (RNi2B2C)